Is there a remedy?

If tightening the drivers doesn't work you will need to find the source of the buzzing. As mentioned above, it might even be something other than the speakers. The problem is that it only occurs when playing very loud. You can't be holding your ear next to a driver while it is producing 120 dB at close range. My recommendation is to buy a pair of Etymotic Research ER20 earplugs available on Amazon (and elsewhere). They are designed to reduce the sound level more uniformly across the frequency spectrum.

If you or anyone you know ever attends live amplified music shows these earplugs are absolutely wonderful. You can hear everything while saving your hearing. They also make great stocking stuffers!

When I had my recording studio I bought them in quantity directly from Etymotic. I gave them to the members of the bands I recorded (I did a lot of metal and hardcore) along with a lecture about preserving their hearing. The Etymotic guy asked what I was doing with them and when I told him he gave me an extra discount. Great people.

Treynolds155 gives excellent advice. I just sent a text to an audio buddy of mine last night suggesting that he tighten the driver fasteners on his speakers. You wouldn't think they would be loose in the first place and you wouldn't think it would make that big of a difference in the sound and you would be wrong on both counts. It's a good place to start and at the very least you will get a much tighter and more focused sound if they are even slightly loose

Maybe start off by tightening the driver fasteners first? The do get a bit loose over time. 

+1 on Cabinet/driver/wire are the most likely culprits

I had internal wire buzz in martin logans in both speakers. The wires will buzz either against the driver, cabinet or the crossover components. Fixed it with self adhesive weather tape in the places where wire was close to other components.

@baylinor LMAO, oops, typo, I meant +1 

If it for sure is cabinet/driver/wire buzz then the suggestions are competent.  I experienced an omnidirectional buzz for weeks.  Turned out it was a ceiling heating vent.  Dampened it with poster putty.  Best of luck solving.  Cheers

Ask Kenjit.

Buy some automotive sound deadening material like boom mat or norez. But make sure there there isn't something loose first. 

A buzz is usually a bad driver or a wire touching the speaker cone/element. Try to isolate if you can.

Is the front baffle removable?

The drivers look to be rear mounted and I do not see access to inside the cabinet (even @ the binding posts).

DeKay

That would drive me crazy. I would sell them and buy something better made. I would justify it as being "economical". 

It could be something pretty stupid, like a wire flopping around or insualtion.  If you feel like pulling a driver out and looking it might be worthwhile.

The bracing is all on the inside, so there’s probably little you can do. Maybe if something starts to buzz In let’s say 10 years, you could trade them in.😁

All the best?